K. Pearson 
191 
normal curve to a symmetrical binomial in a totally different manner. I succeeded 
in showing that the ordiuates and areas of the normal curve gave exceedingly 
closely the terms and sums of terms of the syn\met]ical binomial even for 
relatively small values of n. This had already been done by Laplace. The reader 
will realise this if he looks at the closeness of the normal curve with 
<T - \/Npq = WN, 
and the binomial (2 + 2)'" ^^i*'^ iV^=10 in the accompanying Figure 8. But my 
method enabled me to give a simpler expression to the asymmetrical binomial 
I 3 J 4 e e 7 8 9 10 11 12 
Number of Binomial Terms. 
Fig. 3. Comparison of Point Binomial 1024 (J + with the Gaussian Curve. 
H.D. = ^Npq -l-oSn. Maximum Ordinate 2.58-35. 
than had been obtained by Poisson or Edgevvorth using Stirling's theorem. 
Figure 4 shows how closely the terms of the asymmetrical binomial 5000 + ^Y" 
and the sums of terms are reproduced by n)y curve of Type III., i.e. 
y/= 1536-54 (1 + 1^6-'=". 
I had no higher ambition^ — nor could I have had one higher — than Laplace had 
when he discovered the normal curve. I wanted to find a close mathematical 
expression for the terms of the asymmetrical binomial for relatively small values 
of N. 
Now Laplace and Poisson had both retained the last of Gauss's limiting 
conditions, i.e. they had by adopting the binomial supposed each increment of the 
deviation to be independent of previous increments. It seemed needful to me to 
get rid of this condition, and I therefore introduced instead of the binomial the 
hypergeometrical series. Here the successive increments are correlated. In order 
